Applicant's prior patents U.S. Pat. No. 8,472,534 entitled “Telecommunication Signaling Using Non-Linear Functions” and U.S. Pat. No. 8,861,327 entitled “Methods and Systems for Communicating”, the contents of which are herein incorporated by reference in their entirety, introduced spiral-based signal modulation. Spiral-based signal modulation may base signal modulation on complex spirals, rather than the traditional complex circles used by standard signal modulation techniques such as Quadrature Amplitude Modulation (QAM) and Phase-Shift Keying (PSK).
In spiral modulation, symbol waveforms may be constructed by multiplying a complex circle, whose period may correspond to the symbol time, by a sequence of real amplitude values that may vary over the symbol time. To avoid boundary amplitude discontinuities, these amplitude values may first increase then decrease over the symbol time, returning to the initial amplitude. Symbol waveforms may be distinguished from each other by this amplitude variation, a technique that may be called “intra-symbol amplitude modulation”. Standard modulation techniques, such as phase modulation, may be additionally applied.
Intra-symbol amplitude modulation provides new ways to distinguish between symbol waveforms, and therefore to potentially improve communication performance. However, certain inefficiencies may still be present in existing intra-symbol amplitude modulation-based communication methods, and further refinements to intra-symbol amplitude modulation-based communication technology may still be made.